Question: Solve for $x$ : $x^2 + 5x - 50 = 0$
The coefficient on the $x$ term is $5$ and the constant term is $-50$ , so we need to find two numbers that add up to $5$ and multiply to $-50$ The two numbers $-5$ and $10$ satisfy both conditions: $ {-5} + {10} = {5} $ $ {-5} \times {10} = {-50} $ $(x {-5}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 10) = 0$ $x - 5 = 0$ or $x + 10 = 0$ Thus, $x = 5$ and $x = -10$ are the solutions.